We numerically investigate a stable propagation regime of soliton pulse trains in fibers with periodically copensated loss by lumped optical amplifiers. When amplification solition pulses is 1.2~1.5 and the minimum soliton separation normalized by the soliton width becomes about 6. In cases of L=50[km], the allowable range of A is 1.5~1.7 under =6. The maximum allowable variation of the loss compensation in each lumped amplifier becomes +-2% of the fiber loss when L=50[km], A=1.6, and =6. Generally, the allowable rages of the soliton amplitude A and amplifier gain are inversely proportional to the amplification period L.